do they mean the same thing? If not, then what\'s the difference? Solution ANSWER: Probability Density Function describes the relative likelihood for this random variable to occur at a given point in the observation space. The probability of a random variable falling within a given set is given by the integral of its density over the set. Distribution Function describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.